Preheat the oven to 350 degrees F (175 degrees C).
Whip egg in a medium bowl until foamy. Add leftover stuffing. Cube 4 pieces of Cheddar cheese, about 1/2 inch in diameter, and set aside. Shred the remaining Cheddar cheese. Add shredded cheese to stuffing mixture. Mix well.
Spoon half of the stuffing mixture into 4 muffin cups. Use your finger to create a small indention, add a piece of cubed cheese, and cover with remaining stuffing mixture.
Bake in the preheated oven until tops spring back when lightly pressed, about 27 minutes. Cool in the tin for 5 minutes. Transfer to a wire rack to cool completely.